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Mathematics · Sets and Relations

JEE Main 2024 — 6 April, Shift 2 — Question 2

Let A={1,2,3,4,5}\mathrm{A}=\{1,2,3,4,5\}. Let R be a relation on A defined by xRyx R y if and only if 4x≤5y4 x \leq 5 y. Let mm be the number of elements in R and n be the minimum number of elements from A×A\mathrm{A} \times \mathrm{A} that are required to be added to R to make it a symmetric relation. Then m+n\mathrm{m}+\mathrm{n} is equal to:

  1. Option A:

    24

  2. Option B:

    23

  3. Option C:

    25

    Correct
  4. Option D:

    26

Answer: C

Step-by-step solution

Given : 4x≤5y4 \mathrm{x} \leq 5 \mathrm{y}

then

R={(1,1),(1,2),(1,3),(1,4),(1,5),(2,2),(2,3),(2,4),(2,5),(3,3),(3,4),(3,5),(4,4),(4,5),(5,4),(5,5)}\mathrm{R}=\{(1,1),(1,2),(1,3),(1,4),(1,5),(2,2),(2,3),(2,4),(2,5),(3,3),(3,4),(3,5),(4,4),(4,5),(5,4),(5,5)\}

i.e. 16 elements

i.e. m=16\mathrm{m}=16

Now to make R a symmetric relation add

{(2,1)(3,2)(4,3)(3,1)(4,2)(5,3)(4,1)(5,2)(5,1)}\{(2,1)(3,2)(4,3)(3,1)(4,2)(5,3)(4,1)(5,2)(5,1)\}

i.e. n=9\mathrm{n}=9

So m+n=25\mathrm{m}+\mathrm{n}=25

Answer key and solution verified before publishing.

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Exam
JEE Main 2024
Paper
6 April, Shift 2
Subject
Mathematics
Chapter
Sets and Relations
Topic
Types of Relations
Let A =\ 1,2,3,4,5\ . Let R be a relation on A defined by x R y if… | JEE Main 2024 PYQ with Solution · DhiX AI